I don't have Stick Control near me at the moment, but generally you can count through
tied notes as if there wasn't anything special, and just not play the tied note (the 2nd).
Generally in music a tied note would mean holding the note longer, but on drums it just
means waiting longer until the next stroke follows. Tied notes aren't really necessary for
rhythmical instruments, because we normally don't sustain notes on purpose.
Yes and no, Swiss. On timpani, for example, the length of the note is often adjusted by muting. That's also a achievable on snare drums and tom toms using various techniques if you want to get precise. I've been known to mute the sustain of my snare and toms with my hands or sticks when I'm playing a note that needs to be cut off to leave silence along with the band. Alternatively, I'll use buzzes to lengthen notes. Honouring the length of the note is definitely possible with cymbals and with hihats (open/closed), etc. A bass drum can be muted/shortened or lengthened by burying the beater or allowing it to come out, depending on your tuning/muffling. Check out this guy using mute/open tones on his floor tom to mimic a surdo, for instance:
http://www.youtube.com/watch?v=L1uw7ZCC9L4
I also think it's really important from a musical standpoint for drummers to learn to hear the length of notes the same way a horn player or singer would so that we can accompany those parts well and in a commensurate style.
Take the case of four swung eighths ending with a tie to the following quarter compared to four eighths followed by a rest. There is a big difference between how I would play the first one: Do-vi-doo-AHH, and the second: Do-vi-do-DAT. Those aren't the same rhythm and in the first case I'd be far more likely to use a
sostenuto sound like shoulder crash on a ride, or a crash cymbal to mimic the length that the horns are playing, whereas in the former case I'd be more likely to use a sharp, precise sound like a rimshot jab on the SD or a BD.
Moreover, I find that hearing the length of notes (ties and dots included) helps my time and feel. I was encouraged to sing the full length of note when learning to read and play, and I make my students do it, too. I think this helps connect us to a more lyrical and melodic conception of what we're playing. The same way singing subdivisions will fill the space between notes, giving the note it's whole length and breadth has the same effect.
Here's another example. A dotted-eighth-sixteenth rhythm (dots act like ties) has a different feeling and phrasing than a sixteenth followed by two sixteenth rests and a sixteenth note. Sing the two to yourself giving the notes their correct length and you'll hear the tendency to think of the second one in a more staccato fashion. There's also the tendency to weight both notes evenly, whereas in the dotted-eighth-sixteenth rhythm, even in the absence of accent markings, we'll still tend to put more weight into the first note. The difference in feel between playing both notes at equal dynamic and playing the long note with even just a smidgen more weight is massive. Record yourself playing a groove with each as the ostinato and see if you hear it. I think the conception we have in our heads makes its way into the sound we're making on the drums. As I mentioned earlier, trying playing the first rhythm using a buzz and a single stroke as an example of how we might play the length of the note as a melodic instrument would. Or use an open and closed Hihat to play both rhythms. They aren't alike in the slightest.
Also, without ties and dots, the page would be cluttered with a lot more devilish little rests, which are murder on the eyes.